I noticed that in $Version == "13.2.0 for Mac OS X x86 (64-bit) (November 18, 2022)" Mathematica has conflicting FiniteGroupData for {"PointGroup", "O"}.

Evidence of the bug is that Length[FiniteGroupData[{"PointGroup", "O"}, "ConjugacyClasses"]] != Length[FiniteGroupData[{"PointGroup", "O"}, "ConjugacyClassNames"]].

It turns out the ConjugacyClasses are correct but the ...Names are not. The bug is that

{E,6Subscript[C, 4],3Subscript[C, 2] 8Subscript[C, 3],6Subsuperscript[C, 2, \[Prime]]}

looks to the eye like a list of length 5, but the third and putative fourth elements are not comma separated. They happen to be in the correct order by looking at the ConjugacyClasses themselves.

I checked every finite group, not judging missing data.

comparison = Table[{G, FiniteGroupData[G, #] & /@ {
    {G, FiniteGroupData[]}];
comparison = comparison /. {
    Missing["TooLarge"] -> Nothing, 
    Missing["NotAvailable"] -> Nothing
problems = Select[comparison, Not[Equal[#[[2]]]] &]

The final result is that

problems[[All, 1]] == {{"PointGroup", "O"}, {"PointGroup", "Th"}}

This is not the first elided-comma bug I have found in FiniteGroupData.

  • 1
    $\begingroup$ I have submitted a bug report to Wolfram Support. $\endgroup$
    – evanb
    Nov 15, 2023 at 10:31

2 Answers 2


A temporary workaround is

FiniteGroupData[{"PointGroup", "O"}, "ConjugacyClassNames"] = (
    FiniteGroupData[{"PointGroup", "O"}, "ConjugacyClassNames"] /. Times -> Sequence
FiniteGroupData[{"PointGroup", "Th"}, "ConjugacyClassNames"] = Flatten@(
    FiniteGroupData[{"PointGroup", "Th"}, "ConjugacyClassNames"] /. Times -> Reverse@*List

In $Version == "14.0.0 for Mac OS X ARM (64-bit) (December 13, 2023)" the example now yields problems == {}; the bug is fixed.


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